Problem: Simplify the following expression: $\sqrt{52} - \sqrt{13}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{52} - \sqrt{13}$ $= \sqrt{4 \cdot 13} - \sqrt{13}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{13} - \sqrt{13}$ $= 2\sqrt{13} - \sqrt{13}$ Finally, simplify by combining the terms. $= ( 2 - 1 )\sqrt{13} = \sqrt{13}$